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Question: The value of \({{k}_{w}}\)in a neutral solution is \(5.474\times {{10}^{-14}}\,\)at 50 degrees. Calc...

The value of kw{{k}_{w}}in a neutral solution is 5.474×10−14 5.474\times {{10}^{-14}}\,at 50 degrees. Calculate the pH of the solution at this temperature.

Explanation

Solution

Before solving this question, we should first know about the formula to calculate pH.
pH = −log⁡ (H+)-\log \,({{H}^{+}}) and kw{{k}_{w}}= (H+) (OH−)({{H}^{+}})\,(O{{H}^{-}})and as the solution is neutral, therefore (H+)= (OH−)({{H}^{+}})=\,(O{{H}^{-}}). Now, we can apply this formula and solve the numerical easily.

Complete answer:
To find the pH of this solution, we have to use two formulas-
First of equilibrium constant :
kw= (H+)(OH−){{k}_{w}}=\,({{H}^{+}})(O{{H}^{-}})
The second is of pH :
pH=−log⁡(H+)pH=-\log ({{H}^{+}})
The first thing to do is to calculate the concentration of (H+)({{H}^{+}}) ions that is present in the water at a particular temperature.
As It is mentioned: The solution is neutral .
Therefore,the concentration of (H+)({{H}^{+}}) ions = The concentration of (OH−)(O{{H}^{-}})ions
kw= (H+)(OH−){{k}_{w}}=\,({{H}^{+}})(O{{H}^{-}})
kw= (H+)(H+){{k}_{w}}=\,({{H}^{+}})({{H}^{+}})
Now, there will be a square of (H+)({{H}^{+}}) ions
kw= (H+)2{{k}_{w}}=\,{{({{H}^{+}})}^{2}}
For the concentration of (H+)({{H}^{+}}) ions, we have to square root kw{{k}_{w}} .
In This question kw{{k}_{w}}is given as 5.474×10−14 5.474\times {{10}^{-14}}\,
So, 5.474×10−14 5.474\times {{10}^{-14}}\, = (H+)(H+)=\,({{H}^{+}})({{H}^{+}})
H+= 5.474×10−14{{H}^{+}}=\,\sqrt{5.474\times {{10}^{-14}}}
= 2.339×10−72.339\times {{10}^{-7}}M
Now, we have to apply the formula of pH:
pH=−log⁡(H+)pH=-\log ({{H}^{+}})
= − log⁡(2.339 ×10−7)=\,-\,\log (2.339\,\times {{10}^{-7}})
= 6.630
So, the pH of the solution at temperature is 6.630.

Additional Information:
pH has various uses like
Hydrochloric acid in our stomach helps to digest the food without damaging our stomach. But if the concentration of acid exceeds a certain limit, then we face problems like pain and indigestion. SO, to neutralize it Antacids are taken to balance the pH.
Soils need a certain amount of pH to be fertile. The soil should not be too acidic or too alkaline. It hampers the growth of the plant.

Note:
The calculation of the Acidity or alkalinity of a solution is known as pH. The relative quantity (H+)({{H}^{+}}) is stated by pH. Acidity depends on the concentration of the (H+)({{H}^{+}}) ions. If the concentration of(H+)({{H}^{+}}) ions is more then more is the acidity of the solution.